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California Consumer Notice

Write an Equation When Given Its Solutions

The calculator generates quadratic and cubic equations from its solutions using Vieta's formulas.

Enter solutions to the equation
Number of solutions

x1 =

x2 =


Vieta's formulas

Write a Quadratic Equation When Given Its Solutions

If x 1 and x 2 are the roots of the quadratic equation ax 2 + b x + c = 0 then:
x 1 + x 2 = - b a
x 1  ·  x 2 = c a


If x 1 and x 2 are the roots of the quadratic equation x 2 + p x + q = 0 then:
x 1 + x 2 = - p
x 1  ·  x 2 = q

Write a Cubic Equation When Given Its Solutions

If x 1 , x 2 and x 3 are the roots of the cubic equation a x 3 + b x 2 + c x + d = 0 then:
x 1 + x 2 + x 3 = - b a
x 1 x 2 + x 1 x 3 + x 2 x 3 = c a
x 1  ·  x 2  ·  x 3 = - d a


See also